facia is 3- 2 by 6's and joist hangers are used to hold rafters on to it. will work but use it if no head room. and 3- 2 by 6 should be about (in snow country) 4 to 5 feet span.

you will have to cut angle the top of the beam.

and this all depends on a low pitch of the roof. a higher pitch will require 2 by 10's as the inner part of the beam. these will show below. but will have more strength and make the building department more happy.